Thread by @stevenstrogatz

In this more sophisticated convention, which is often used in algebra, implicit multiplication (also known as multiplication by juxtaposition) is given higher priority than explicit multiplication or explicit division (in which one explicitly writes operators like × *  / or  ÷).

Under this more sophisticated convention, the implicit multiplication in 2(2+2) is given higher priority than the explicit division implied by the use of ÷.

That’s a very reasonable convention, and I agree that the answer to the original question is 1 if we are using that convention.

But that convention is not universal, e.g., the calculators in Google and WolframAlpha use the less sophisticated convention that I described; they make no distinction between implicit and explicit multiplication when they are asked to evaluate simple arithmetic expressions.

In particular, the calculators in Google and WolframAlpha interpret 8÷2(2+2) as 8÷2×(2+2) and therefore evaluate this as 16.  

For my article, I chose to focus on this simpler convention. 

Hope this helps! Thanks to you all for your comments.